ECO 2404 – Assignment 2
英国eco经济学代写 Download the data “data-olley-pakes”. There are 531 firms and 6 years of data. Each row refers to one firm in one year.
1 EstimatimgProductiom Fumctiom
Download the data “data-olley-pakes”. There are 531 firms and 6 years of data. Each row refers to one firm in one year. The variables are as follows: firm, year, output, age, capital, labor, and investment. If a firm‘s values are zero in a given year, that means that the firm does not exist in that year, it has either exited already or not yet entered.
You can answer the questions using either STATA or MATLAB, although I would suggest you to implement the Olley and Pakes (OP) estimator in MAT- LAB to have a better understanding of the method. If you are using STATA, do not forget to change the zeros into dots so that STATA understands that the variables are missing¡ otherwise it will consider the zeros as observations. Make sure you put the data in logs before estimating the model.
1.1 Model 英国eco经济学代写
Assume the firms have a Cobb-Douglas production function (let’s ignore firm’s age in the exercise, but you can include it if you want to):
(1)
where yist is the log of output; lst is the log of labor; kst is the log of capital; the term wit represents “productivity shocks” that are observed or predictable by the firms before making their input decisions at t; and εst represents both i.i.d. shocks to production that are not predicted by the firms and measurement errors in the observed variables. The endogeneity problem in estimating (1) comes from the correlation between the inputs and wit.
1.2 Questiom
1.Estimate the production function using pooled OLS for both the unbal- anced and for the balanced panel data. What do you find? Are the estimatessignificant?Are they economically reasonable? Why would you expect them to be biased?
2. Assume c
, i.e., it is a time-invariant fixed-effect. Estimate the production function using the fixed-effect estimator. What do you find? Are the estimates significant? Are they economically reasonable?
3.Assume 
, where |ρ| < 1 and 
is i.i.d. Add the fixed-effect ai in the unobservables. Estimate the production function using the SYS GMM estimator proposed by Blundell and Bond. What do you find? Are the estimates significant? Are they economically reasonable?
4.Return to the original model (1) and assume the model satisfies the OP assumptions. Estimate the model using investments as a proxy forcst. 英国eco经济学代写
(a)Estimate the first step of OP to get 
. Use a fourth order polynomial series (just as OP did) for Øst.
(b)Estimatethe second step of OP ignoring the selection problem to get
. Use a fourth order polynomial to approximate the function g (.), where
and use the vector of instruments (1, hst)t.
(c)Whencompared with your previous results (OLS, FE, and SYS GMM), does your new estimate from OP conform with the biases suggested by the theoretical model?(d)Calculate productivity growth for each firm as in Olley and Pakes (1996), Section 5:
Calculate aggregate productivity growth for the sample in each year using output shares to aggregate firms (
), and do the same decomposition as they perform (equation 16). What do you conclude in terms of relocation of output shares versus plant- level growth?
(e)(EXTRA) You do not need to incorporate the selection problem into OP, but you can if you want In this case, when you estimate the survival probability function (i.e., the probability of staying in the market) you may use a fourth order polynomial within a pro-bit model, Pst=( 
). Then, in the last step (the nonlinear least squares), also use a fourth order polynomial for g (.), where now
Discuss your estimates compared with those obtained ignoring the selection problem. 英国eco经济学代写
HINT 1: There are a couple of ways to handle the unbalanced panel in MATLAB. One possibility is to first drop all missing data (all the lines with zeros) and then estimate the model as usual. To create lagged variables you need to be careful. One possibility is to first shift the whole vector (create in MATLAB the yit-1 as “y_1=[0,y];”)Then, you replace with zeros all lines in which year = 1 (so that the lagged variable for the firms’ first year is zero and not the previous firms’ last observation). Finally you drop the lines with zeros when estimating βk and g (.).
HINT 2:If you want to correct for selection,you need to estimate the prvobit 
befove dvopsng the missing variables in MATLAB. It may be easier to estimate Pit in STATA, save the results and then move to MATLAB. 英国eco经济学代写
OBS: Note that the usual standard errors in the second stage will be wrong since they need correction for the error in the first stage estimators. This can be done analytically (using Pakes and Olley (1995)), or it can be “bootstrapped”. Don’t worry about the corrections needed.
